New answers tagged


As described above, the first player loses if $N$, the initial number of marbles, is a Fibonacci number, and wins for any other integer $N > 1$. Proof follows. First, a definition. The remainder of any integer $k$ is the smallest entry in a list of distinct non-consecutive Fibonacci numbers that add up to $k$. (For Fibonacci numbers, the remainder of $...

Top 50 recent answers are included